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The hydrodynamics of locomotion at intermediate Reynolds numbers: undulatory swimming in ascidian larvae (Botrylloides sp.)
1 Department of Integrative Biology, University of California, Berkeley, CA
94720, USA
2 Organismic and Evolutionary Biology Program, 221 Morrill Science Center,
University of Massachusetts, Amherst, MA 01003, USA
* Author for correspondence at present address: The Museum of Comparative Zoology, Harvard University, 26 Oxford St, Cambridge, MA 02138, USA (e-mail: mchenry{at}fas.harvard.edu)
Accepted 10 October 2002
Understanding how the shape and motion of an aquatic animal affects the
performance of swimming requires knowledge of the fluid forces that generate
thrust and drag. These forces are poorly understood for the large diversity of
animals that swim at Reynolds numbers (Re) between 100 and
102. We experimentally tested quasi-steady and unsteady
blade-element models of the hydrodynamics of undulatory swimming in the larvae
of the ascidian Botrylloides sp. by comparing the forces predicted by
these models with measured forces generated by tethered larvae and by
comparing the swimming speeds predicted with measurements of the speed of
freely swimming larvae. Although both models predicted mean forces that were
statistically indistinguishable from measurements, the quasi-steady model
predicted the timing of force production and mean swimming speed more
accurately than the unsteady model. This suggests that unsteady force (i.e.
the acceleration reaction) does not play a role in the dynamics of steady
undulatory swimming at Re
102. We explored the relative
contribution of viscous and inertial force to the generation of thrust and
drag at 100<Re<102 by running a series of
mathematical simulations with the quasi-steady model. These simulations
predicted that thrust and drag are dominated by viscous force (i.e. skin
friction) at Re100 and that inertial force (i.e. form
force) generates a greater proportion of thrust and drag at higher Re
than at lower Re. However, thrust was predicted to be generated
primarily by inertial force, while drag was predicted to be generated more by
viscous than inertial force at Re102. Unlike swimming
at high (>102) and low (<100) Re, the
fluid forces that generate thrust cannot be assumed to be the same as those
that generate drag at intermediate Re.
Key words: swimming, intermediate Reynolds number, morphology, larvae, ascidian, urochordata, Botrylloides sp
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